Summary
Based on the budget of kinetic energy and simple estimates to relate dissipation and temperature or concentration fluctuations to shear, stratification, and the vertical velocity fluctuations, a consistent set of equations is deduced to estimate vertical fluxes of momentum and heat or mass. The estimates are designed for strongly sheared, neutral and stratified flows at high Reynolds numbers under approximately homogeneous conditions. The set is closed by using basically two empirical coefficients together with the turbulent Prandtl number and the growth rate of kinetic energy as a function of the gradient Richardson number. The correlations are tested using data from previous laboratory experiments and numerical simulations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hunt, J.C.R., Kaimal, J.C., Gaynor, J.E.: Some observations of turbulence structure in stable layers. Q.J.R. Meteorol. Soc. 111, 793–815 (1985).
Lilly, D.K., Waco, D.E., Adelfang, S.I.: Stratospheric mixing estimated from high-altitude turbulence measurements. J. Appl. Meteorol. 13, 488–493 (1974).
Osborn, T.R.: Estimates of the rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83–89 (1980).
Rohr, J.J., Itsweire, E.C., Helland, K.N., Van Atta, C.W.: Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech. 195, 77–111 (1988).
Tavoularis, S. Corrsin, S.: Experiments in nearly homogeneous turbulent shear flow with a uniform temperature gradient. Part 1. J. Fluid Mech. 104, 311–347 (1981).
Tavoularis, S., Corrsin, S.: Effects of shear on the turbulent diffusivity tensor. Int. J. Heat Mass Transfer 28, 256–276 (1985).
Tavoularis, S., Karnik, U.: Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence. J. Fluid Mech. 204, 457–478 (1989).
Hunt, J.C.R., Stretch, D.D., Britter, R.E.: Length scales in stably stratified turbulent flows and their use in turbulence models. In: Stably stratified flows and dense gas dispersion (Puttock, J. S., ed.), pp. 285–321. Oxford: Clarendon Press 1988.
Kaltenbach, H.-J.: Turbulente Diffusion in einer homogenen Scherströmung mit stabiler Dichterschichtung. Diss. TU München, Report DLR-FB 92–26, p. 142 (1992).
Gerz, T., Schumann, U., Elghobashi, S.E.: Direct numerical simulation of stratified homogeneous turbulent shear flow. J. Fluid Mech. 200, 563–584 (1989).
Nieuwstadt, E. T. M.: The turbulent structure of the stable, nocturnal boundary layer. J. Atmos. Sci. 41, 2202–2216 (1984).
Zierep, J.: Ähnlichkeitsgesetze und Modellregeln der Strömungslehre, p. 138. Karlsruhe: G. Braun, 1972.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag
About this chapter
Cite this chapter
Schumann, U. (1994). Correlations in homogeneous stratified shear turbulence. In: Schnerr, G.H., Bohning, R., Frank, W., Bühler, K. (eds) Fluid- and Gasdynamics. Acta Mechanica, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9310-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-7091-9310-5_12
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82495-5
Online ISBN: 978-3-7091-9310-5
eBook Packages: Springer Book Archive